MindMap Gallery Sinusoidal AC Circuits – Basic Concepts
Some basic concepts of alternating current analysis in electronic circuits, including: mathematical basis of circuits, classification, and vector representation of sinusoidal quantities. Hope this helps.
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sinusoidal ac circuit
basic concept
Mathematical basis
sinusoidal quantity
Three elements
Amplitude: The maximum instantaneous value of alternating current. The amplitude must be represented by a capital letter subscript plus m, which determines the size.
Angular frequency: changes in radians per second. Unit: rad/s, determines the speed of change
Initial phase: determine the initial position
Phase:
Three parameters representing how fast the sinusoidal quantity changes
Period T, unit s
Frequency f, unit Hertz Hz
Angular frequency w, unit ead/s
The relationship between the three:
The relationship between two sinusoidal quantities (note the comparison here are of the same frequency)
lead and lag
In-phase and anti-phase, orthogonal
Plural numbers and their expressions
algebraic form
Real part and imaginary part:
mold:
The angle between the complex number A and the real axis:
The relationship between a, b and module
trigonometric form
exponential form
Euler's formula:
Exponential form of complex numbers:
Polar form
Operations on complex numbers: assuming two complex numbers
Addition and Subtraction: Using Algebraic Form
Multiplication and division:
rotation factor
Classification
Instantaneous value:
Basic representation: lowercase letters:
Valid values
Definition: A DC current and an AC current pass through resistors of equal resistance respectively. If the energized If the time is equal, the heat generated on the resistor is also equal, then the value of direct current is called alternating current. Effective value of current
formula:
Maximum value: represented by capital letter subscript plus m
Vector representation of sinusoidal quantities: For sinusoidal quantities of the same frequency, Characterizing different sinusoidal quantities only requires the maximum value (or effective value) and initial phase.
The current and voltage are respectively
Maximum phasor
rms phasor
phasor diagram
The phasors represented by sinusoidal quantities of the same frequency can be drawn on the same picture.
Add vectors according to the parallelogram rule
https://www.zhihu.com/equation?tex=\omega=2\pi f